Resistor R16 fails open: Output code will be 15 (1111) all the time.

Resistor R1 fails open: If Vin < Vref, output will be 0 (0000); if Vin > Vref, output will be 15 (1111).

Comparator U13 output fails low: Output will assume the 13 state (1101) unless Vin exceeds that analog value, then the ADC will register properly.

Solder bridge (short) across resistor R14: There will be no distinctive 13 state (1101), the analog values for all the other states adjusting slightly to fill the gap.